Menger remainders of topological groups

作者：Bella Angelo; Tokgoz Secil; Zdomskyy Lyubomyr^*

来源：Archive for Mathematical Logic, 2016, 55(5-6): 767-784.

DOI：10.1007/s00153-016-0493-8

• Remainder
• Topological group
• Menger space
• Hurewicz space
• Scheepers space
• Ultrafilter
• Forcing

In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it is -compact. Also, the existence of a Scheepers non--compact remainder of a topological group follows from CH and yields a P-point, and hence is independent of ZFC. We also make an attempt to prove a dichotomy for the Menger property of remainders of topological groups in the style of Arhangel'skii.

• 出版日期2016-8